如果有理数a、b满足Ia-2I+I1-bI=0求下列式子的值1/ab+1/(a+1)(b+1)+1/（a+2)(b+2)+...+1/(a+100)(b+100)

题目

如果有理数a、b满足Ia-2I+I1-bI=0求下列式子的值1/ab+1/(a+1)(b+1)+1/（a+2)(b+2)+...+1/(a+100)(b+100)

答案

Ia-2I+I1-bI=0
则a-2=0,1-b=0
得a=2,b=1
1/ab+1/(a+1)(b+1)+1/（a+2)(b+2)+...+1/(a+100)(b+100)
=1/2+1/(2×3)+1/(3×4)+…………+1/(101×102)
=1/2+1/2-1/3+1/3-1/4+…………+1/101-1/102
=1/2+1/2-1/102
=1-1/102
=101/102